Note that the rank \(R\)  does not depends on the chosen of the orientation. Denoting by \(n_i(\mathcal {G})\)  the number of bubbles in \(\mathcal {G}\)  with \(2i\)  black and white nodes, the divergences subgraphs are said to be melonic [1]}, [2]}, if and only if they satisfy the following relation:
\(F(\mathcal {G})-R(\mathcal {G})=3(L(\mathcal {G})-\sum _in_i(\mathcal {G})+1)\) 
